1. Field of the Invention
The present invention is related to communication systems. More particularly, the present invention is related to wireless communication systems having multiple transmitter and receiver antennas.
2. Discussion of the Related Art
This section is intended to introduce the reader to various aspects of art that may be related to various aspects of the present invention, which are described and claimed below. This discussion is believed to be helpful in providing the reader with background information to facilitate a better understanding of the various aspects of the present invention. Accordingly, it should be understood that these statements are to be read in this light, and not as admissions of prior art.
Over the past several decades, the wireless communications industry has grown at an incredible rate. The convenience and usefulness of wireless communications cannot be understated. Indeed, the devices which use the wireless communication systems, including cell phones, personal digital assistants, and notebook computers, have become nearly ubiquitous. People are using the devices at all times of the day, for business and leisure.
In an effort to increase the usefulness and convenience of the devices, the wireless communications industry is a continuously seeking to increase the capacity of wireless systems. One way of increasing the capacity of a wireless communication system is configuring the system to have multiple antennas at both the transmitters and receivers. Such systems are commonly referred to as multiple-input multiple output (MIMO) systems. The MIMO systems are capable of achieving increased capacity compared to systems implementing only single antennas at either the receiver or transmitter by using preceding techniques. The preceding techniques reduce or eliminate interference between different receiver antennas using measurements of a channel transfer matrices of pilot beams transmitted by the transmitter. The measurements are fed back to the base station and, generally, the information about channel vectors provided by the measurements allows a dramatic increase in the throughput of the entire system.
It has been suggested each mobile device use a quantization code book C consisting of 2B complex M-tuples of norm one, where B represent the number of bits sent as feedback to the base station and M represents the number of base station transceivers. Stated mathematically:C={c1, . . . , c2B},ciεCM,∥ci∥=1  (1).Each mobile device, therefore, performs the following steps:                1) Defines a vector space Q spanned by its channel vectors h1, . . . , hNεCM, where N is the number of transceivers at the mobile, i.e.:Q=span(h1, . . . , hN)={a1h1+ . . . +aNhN:a1, . . . , aNεC},  (2);        2) Finds a code vector crεC that has the minimum angle between the code vector and Q, i.e. it finds:r=arg mincjεC{|∠(cj,Q)|},  (3); and        3) Transmits the index r to the base station.        
After receiving the feedback information, indexes r from all mobile devices in the wireless communication devices, the base station uses a precoding technique for broadcasting information to the mobile devices. For example, a zero-forcing preceding technique may be used, such as that disclosed in “On the Achievable Throughput of a Multiantenna Gaussian Broadcast Channel,” by G. Caire and S. Shamai, published in IEEE TRANS. INFORM. THEORY, vol. 49, pp. 1691-1706, July 2003; and “A Feedback Reduction Technique for MIMO Broadcast Channels” Jindal, N.; INFORMATION THEORY, 2006 IEEE INTERNATIONAL SYMPOSIUM, pp. 2699-2703, July 2006, available at http://ieeexplore.ieee.org/xpl/RecentConjsp?punumber=4035458. Both of the above mentioned articles are incorporated herein by reference.
Unfortunately, the brute force implementation of step 2 of the above algorithm has a high level of complexity and is computationally burdensome. For example, if 20 bits are transmitted back to the base station, i.e., B=20, C becomes 220 M-tuples of norm one which is prohibitively too many, and step 2 becomes too complex. The reason for the high complexity of step 2 is that the subspace Q is multidimensional. The channel vectors h1, . . . , hN are random vectors and, therefore, the dimension of Q is a random number. Typically, the dimension of Q will be equal to N, which represents the number of receivers of a mobile device. There are no fast algorithms for searching among the code vectors of the codebook C to find the code vector with the smallest angle between the vector and the multidimensional space Q. As such, using contemporary techniques, the measurements may require extensive hardware and/or software in the receiver and/or extensive processing time in the receiver. However, only a limited amount of time and resources are available for any feedback transmission from a receiver. Specifically, a mobile device only has time to send few bits back to the base station.